Digital-to-analog converter

ABSTRACT

An analog-to-digital converter has a resistor string that generates a series of voltages. An upper selector selects voltages at the upper end of the series. A lower selector selects voltages at the lower end of the series. A pair of midrange selectors select a pair of adjacent voltages in the middle range of the series. A midrange voltage generator generates further voltages spaced between the two selected midrange voltages. An output selector selects one of the further voltages. The selectors are controlled by various bits of a digital input signal. The voltage selected by the upper selector, lower selector, or output selector becomes an analog output signal. This analog-to-digital converter has comparatively few resistors and transistors and can generate accurate voltages for driving a gray-scale display.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation-in-part of application Ser. No.11/640,869 filed on Dec. 19, 2006, which is hereby incorporated for allpurposes.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a digital-to-analog converter (DAC)that generates voltages useful for driving, for example, a liquidcrystal to produce a vivid display.

2. Description of the Related Art

Referring to FIG. 1, a conventional DAC of the type used in a liquidcrystal driving circuit to convert a six-bit digital signal to an analogvoltage signal with sixty-four levels comprises a resistor string thatdivides a reference voltage and outputs sixty-four different voltages,and a switching circuit that selects one of the sixty-four voltagesaccording to the value of the digital input signal.

The resistor string is a string of sixty-three resistors (R1 to R63)connected in series between a lower reference voltage VRL and an upperreference voltage VRH to form a voltage divider. Voltages V0 (=VRL), V1,V2, . . . , V63 (=VRH) at sixty-four different levels are output fromthe two ends and sixty-two interconnection nodes of the resistor string.

The switching circuit is a six-stage binary tree selection circuitcontrolled by six bits b₀ to b₅. Pairs of adjacent voltages V0 and V1,V2 and V3, . . . , V62 and V63 are connected to first-stage switches SW0₁, SW0 ₂, . . . , SW0 ₃₂ and one voltage in each pair is selectedaccording to the value of the least significant bit b₀; the outputs ofpairs of adjacent first-stage switches SW0 ₁ and SW0 ₂, SW0 ₃ and SW0 ₄,. . . are connected to second-stage switches SW1 ₁, SW1 ₂, . . . , andone voltage from each of these pairs is selected according to the valueof bit b₁. Similar selections are made in sequence by third-stageswitches SW2 ₁, SW2 ₂, . . . according to the value of bit b₂,fourth-stage switches SW3 ₁, SW3 ₂, . . . according to the value of bitb₃, and fifth-stage switches SW4 ₁, SW4 ₂, . . . according to the valueof bit b₄, and finally a single analog voltage corresponding to thevalue of the input digital input signal is selected and output as theoutput voltage OUT from switch SW5 according to the value of the mostsignificant bit b₅.

Japanese Patent Application Publication No. 2002-26732 discloses a k-bittwo-stage nonlinear DAC having a first converter that converts the mhighest bits to analog voltages, a pre-charging circuit that prechargesan output load according to a selected one of these analog voltages, anda second converter that converts the n lowest bits to another analogvoltage (m+n=k). This configuration is used to provide increasedconversion speed for an active-matrix liquid crystal display.

A problem with the conventional DACs described above is that the numberof resistors in the resistor string and the number of switches needed toselect the divided voltages increase exponentially. This is a particularproblem nowadays, because the increasing size of liquid crystal displaysdemands a gray scale with more levels for a more vivid color display.This requires an increased number of digital input signal bits,exponentially increasing the area occupied by the resistor string andswitches in the DAC.

Another problem is posed by the large number of signal lines or‘channels’ that are driven through separate switching circuits from asingle resistor string. When the displayed image has a large area of asingle color or gray level, hundreds of channels may be connectedsimultaneously to the same node in the resistor string. In such cases,the combined effect of parasitic wiring resistance or parasitic circuitelements concentrated at a single point in the resistor string cansignificantly distort the output voltages.

In the two-stage nonlinear DAC described above, accuracy is a particularproblem near the upper and lower reference voltage levels, where thegray scale is nonlinear and the voltage differences between adjacentgray levels gradually increase, demanding a gamma correction that thesecond-stage converter cannot provide.

SUMMARY OF THE INVENTION

An object of the present invention is to provide a DAC of the resistorstring type that can provide an increased number of output levels withmore consistent accuracy while occupying a decreased amount of space.

A DAC according to the present invention has a first resistor string forgenerating a series of voltages spanning an upper range, a lower range,and a midrange disposed between the upper range and the lower range.

A lower selector selects one of the voltages in the lower range of theseries as the analog output voltage when the digital input signal has avalue equal to or less than a first boundary value.

An upper selector selects one of the voltages in the upper range of theseries as the analog output voltage when the digital input signal has avalue equal to or greater than a second boundary value.

A pair of midrange selectors select a mutually adjacent pair of voltagesin the midrange of the series when the digital input signal has a valuebetween the first and second boundary values.

A midrange voltage generator generates a further series of voltagesbetween the pair of voltages selected by the midrange selectors. Themidrange voltage generator may be a second resistor string.

An output selector selects one of the voltages in the further series asthe analog output voltage when the digital input signal has a valuestrictly between the first and second boundary values.

The above structure significantly reduces the number of circuit elementsrequired to generate and select midrange voltages, and the number ofcircuit elements needed to select voltages in the upper and lowerranges. Accuracy is improved because of reduced parasitic loads. Gammacorrections can be carried out accurately by confining the midrange tothe linear part of the of the gamma curve.

BRIEF DESCRIPTION OF THE DRAWINGS

In the attached drawings:

FIG. 1 is a circuit diagram of a conventional DAC;

FIG. 2 is a block diagram illustrating the general structure of a DACaccording to the present invention:

FIG. 3 is a graph representing a relationship between display drivingvoltages and brightness in a liquid crystal display;

FIG. 4 is a circuit diagram showing a specific embodiment of the DAC inFIG. 2; and

FIGS. 5A, 5B, and 5C are circuit diagrams showing illustrativeembodiments of the switches in FIG. 4.

DETAILED DESCRIPTION OF THE INVENTION

A DAC embodying the present invention will now be described withreference to the attached drawings, in which like elements are indicatedby like reference characters. For simplicity, parentheses are omitted inthe drawing: for example, V(2^(n)−1) is shown in the drawings as V2^(n)−1.

Referring to FIG. 2, the DAC converts an n-bit digital input signaltaking values from 0 to 2^(n)−1 to an analog output voltage takingvalues from VRL to VRH. The parameter n is a positive integer, and VRHand VRL are externally supplied analog reference voltages. The analogoutput voltage, also referred to below as a driving voltage or grayscale voltage, can be used to drive a picture element in a displaydevice. The DAC comprises a resistor string 1 consisting of a pluralityof resistors connected in series between the lower reference voltage VRLand the upper reference voltage VRH to function as a voltage divider; alower selector 2, an upper selector 3, a midrange upper selector 4, anda midrange lower selector 5 that select voltages output from resistorstring 1; a midrange resistor string 6; and a midrange output selector 7that selects voltages output from the midrange resistor string 6.

At the lower (VRL) end of the resistor string 1, a series of 2^(m)−1resistors with values corresponding to differences between adjacent graylevels generate gray scale voltages V1, V2, . . . , V(2^(m−)1). Thesevoltages and reference voltage VRL, also denoted V0, constitute thelower range of gray scale voltages. The letter ‘m’ designates a positiveinteger less than n, and is equal to the number of switching stages inthe lower selector 2 and upper selector 3.

At the upper (VRH) end of resistor string 1, a series of 2^(m) resistorswith values corresponding to differences between adjacent gray levelsgenerate gray scale voltages V(2^(n)−2), V(2^(n)−3), . . . ,V(2^(n)−2^(m)), V(2^(n)−2^(m)−1). Reference voltage VRH, also denotedV(2^(n)−1), and voltages V(2^(n)−2), V(2^(n)−3), . . . , V(2^(n)−2^(m))constitute the upper range of gray scale voltages.

In the middle part of resistor string 1, a series of resistors withvalues corresponding to 2^(k) gray scale levels (k is equal to orgreater than 2 and less than m) generate gray scale voltagesV(2^(m)−1+2^(k)), V[2^(m)−1+(2×2^(k))], . . . , V(2^(n)−2^(m)−1−2^(k)),V(2^(n)−2^(m)−1), which occupy the midrange. Voltage V(2^(m)−1) is alsoused as part of the midrange, so the midrange and the lower rangeoverlap at this voltage. The boundary values of the digital input signalthat define the midrange are 2^(m)−1 and 2^(n)−2^(m).

The voltages V0, V1, V2, . . . , V(2^(m)−1) in the lower range aresupplied to the lower selector 2, and the voltages V(2^(n)−1),V(2^(n)−2), . . . , V(2^(n)−2^(m)) in the upper range are supplied tothe upper selector 3. Midrange voltages V(2^(m)−1+2^(k)),V[2^(m)−1+(2×2^(k))], . . . , V(2^(n)−2^(m)−1) are supplied to themidrange upper selector 4: midrange voltages V(2^(m)−1),V(2^(n)−1+2^(k)), . . . , V(2^(n)−2^(m)−1−2^(k)) are supplied to themidrange lower selector 5.

The lower selector 2 comprises a group of switches connected in a binarytree configuration to select a gray scale voltage responsive to bits b₀to b_(m) of the digital input signal when bits b_(m+1) to b_(n−1) areall zero (‘0’). The highest voltage that can be selected and output bythe lower selector 2 is V(2^(m)−1). When the digital input signal has avalue of 2^(m) or higher, the output of the lower selector 2 is in thehigh-impedance state, i.e., is switched off; in effect, the lowerselector 2 does not operate.

Similarly, the upper selector 3 comprises a group of switches connectedin a binary tree configuration to select a corresponding gray scalevoltage responsive to bits b₀ to b_(m) of the digital input signal whenbits b_(m+1) to b_(n−1) are all one (‘1’). The lowest gray scale voltagethat can be selected and output by the upper selector 3 isV(2^(n)−2^(m)). When the digital input signal has a value lower than2^(n)−2^(m), the output of the upper selector 3 is switched off.

The midrange upper selector 4 comprises a group of switches connected ina binary tree configuration to select gray scale voltages responsive tobits b_(k) to b_(n−1) in the digital input signal. The selected voltagescorrespond to gray levels at which bits b₀ to b_(k−1) in the digitalinput signal are all one (‘1’). The midrange upper selector 4 can selectand output gray scale voltages from V(2^(m)−1+2^(k)) to V(2^(n)−2^(m)−1)at steps of 2^(k) gray levels.

The midrange lower selector 5 comprises a group of switches connected ina binary tree configuration to select gray scale voltages responsive tobits b_(k) to b_(n−1) in the digital input signal. The midrange lowerselector 5 selects a voltage one resistor step lower, or 2^(k) graylevels lower, than the voltage selected by the midrange upper selector4. Together, the midrange upper selector 4 and midrange lower selector 5select and output a pair of gray scale voltages V[2^(m)−1+(i×2^(k))] andV{2^(m)−1+[(i−1)×2^(k)]} (where i ranges from 1 to 2^(n−k)−2^(m+1−k))responsive to the values of bits b_(k) to b_(n−1) in the digital inputsignal.

The outputs of the midrange selectors 4 and 5 are connected to the twoends of a midrange resistor string 6 consisting of 2^(k) resistors withidentical resistance values connected in series. When the outputs of themidrange selectors 4 and 5 are switched on, accordingly, the midrangeresistor string 6 is connected in parallel with one of the resistors ofresistor string 1. The total resistance of the midrange resistor string6 should be considerably greater (e.g., 1000 times greater) than theresistance of any one resistor in resistor string 1, so as to reduceerrors due to resistance variations when the midrange resistor string 6is switched in and out.

The (2^(k)−1) interconnection nodes in the midrange resistor string 6and the output of the midrange upper selector 4 are connected to theinput side of a midrange output selector 7. The midrange output selector7 comprises a group of switches connected in a binary tree configurationto select one of the voltages output by the midrange resistor string 6,responsive to bits b₀ to b_(k−1) in the digital input signal, and outputthe selected voltage.

When the digital input signal has a value lower than 2^(m) or higherthan 2^(n)−2^(m)−1, the outputs of the three midrange selectors 4, 5,and 7 are in the high-impedance state.

The output terminals of the lower selector 2, upper selector 3, andmidrange output selector 7 are connected to an output terminal 8, fromwhich a gray scale voltage selected by the selectors 2 to 5 and selector7 responsive to the digital input signal is output as an analog outputvoltage OUT.

The relation between gray scale voltage or driving voltage and graylevel or brightness follows the S-shaped gamma curve shown in FIG. 3.Near the upper and lower ends of the gray scale, above V(2^(n)−2^(m))and below V(2^(m)−1), brightness changes gradually more slowly and thusincreases nonlinearly with respect to the driving voltage, but in themiddle region, between V(2^(n)−2^(m)) and V(2^(m)−1), brightness mayincrease (and in this case does increase) linearly.

If the brightness levels in the gray scale are equally spaced, thevoltage difference between adjacent gray levels is not constant, beinglarger at the upper and lower ends of the gray scale than in the middle.Accordingly, when all gray scale voltages are generated by a singleresistor string as in FIG. 1, the resistance values of the resistors inthe middle of the string are comparatively small and substantiallyequal, while the resistance values of the resistors at the upper andlower ends are larger and vary from resistor to resistor.

In FIG. 2, the lower selector 2 and upper selector 3 select gray scalevoltages in the regions where there is a nonlinear relationship betweengray scale voltage and brightness. In the region where the midrangeselectors 4, 5, 7 select the gray scale voltage, there is a linearrelationship between voltage and brightness. The resistance values ofthe 2^(m)−1 resistors at the VRL end of resistor string 1 and the 2^(m)resistors at the VRH end are therefore set according to the nonlinearparts of the curve in FIG. 3 to produce different voltage drops equal tothe individual differences between adjacent gray scale voltage levels.The resistance values of the 2^(k) gray scale level resistors in themiddle section of resistor string 1 are set to equal valuescorresponding to 2^(k) levels in the linear part of the gray scale.

The operation of the DAC shown in FIG. 2 will now be described.

When the value of the digital input signal falls within the range from 0to 2^(m)−1, the outputs of the upper selector 3 and midrange selectors4, 5, 7 are in the high-impedance state. The lower selector 2 selectsone of the voltages from V0 to V(2^(m)−1) generated by resistor string1, corresponding to the value of the digital input signal, and outputsthe selected voltage at the output terminal 8 as the analog outputvoltage OUT.

When the value of the digital input signal falls within the range from2^(n)−2^(m) to 2^(n)−1, the outputs of the lower selector 2 and midrangeselectors 4, 5, 7 are in the high-impedance state. The upper selector 3selects one of the voltages from V(2^(n)−2^(m)) to V(2^(n)−1) generatedby resistor string 1, corresponding to the value of the digital inputsignal, and outputs the selected voltage at the output terminal 8 as theanalog output voltage OUT.

When the value of the supplied digital input signal falls within therange from 2^(m) to 2^(n)−2^(m)−1, the outputs of the lower selector 2and upper selector 3 are in the high-impedance state. The midrange upperselector 4 selects a voltage V[2^(m)−1+(i×2^(k))] for output to theupper end of the midrange resistor string 6. The midrange lower selector5 selects a gray scale voltage V{2^(m)−1+[(i−1)×2^(k)]}, 2^(k) levelslower than the voltage selected by the midrange upper selector 4 in thegray scale, for output to the lower end of the midrange resistor string6. These two voltages are selected according to the most significant n−kbits of the digital input signal and correspond to signal values inwhich the least significant k bits are all one (‘1’). The midrangeoutput selector 7 selects a voltage from among the 2^(k) equally spacedvoltages generated by the midrange resistor string 6, these voltagesranging from V{2^(m)+[(i−1)×2^(k)]} to V[2^(m)−1+(i×2^(k))] at intervalscorresponding to one gray level and being selected according to theleast significant k bits of the digital input signal, and outputs theselected voltage at the output terminal 8 as the analog output voltageOUT.

FIG. 4 is an illustrative embodiment of the DAC in FIG. 2, showing thestructure of the groups of switches in the selectors 2 to 5 and selector7 when n is six, m is three, and k is two (m=6, m=3, k=2). Resistors areindicated by rectangles and switches by squares. The enlarged part ofFIG. 4 indicates the internal structure of a switch SW controlled by abit b_(i) and its inverted value /b_(i): the upper switching element SWhturns on when bit b_(i) is one (‘1’) and /b_(i) is zero (‘0’); the lowerswitching element SW1 turns on when bit b_(i) is zero (‘0’) and /b_(i)is one (‘1’). Switch SW operates as a selector switch. Switches shown inFIG. 4 with no upper or lower connection line function as simple on/offswitches.

If the number of switching elements in switch SW is two, and the numberof switching elements in an on/off switch is one, the total number ofswitching elements in FIG. 4 is ninety, contrasting to one hundredtwenty-six in the conventional DAC shown in FIG. 1. The number ofresistors constituting the two resistor strings is thirty-one in FIG. 4and sixty-three in FIG. 1. These figures indicate that the numbers ofswitching elements and resistors of the DAC in FIG. 4 are significantlyreduced in comparison with the conventional DAC shown in FIG. 1.

FIGS. 5A to 5C are illustrative embodiments of the switches in FIG. 4.

Switching elements SWh and SWl in FIG. 5A are both n-channelmetal-oxide-semiconductor (NMOS) transistors, with their interconnecteddrains functioning for output and their sources functioning for input.The gate of switching element SWh receives a control signal representingbit b_(i); the gate of switching element SWl receives the invertedsignal /b_(i). This type of switch can be effectively used when theanalog voltages to be switched are not too close to the high logic levelof the bit signals b_(i), /b_(i).

Switching elements SWh and SWl in FIG. 5B are both p-channelmetal-oxide-semiconductor (PMOS) transistors, with their interconnecteddrains functioning for output and their sources functioning for input.The gate of switching element SWl receives a control signal representingbit b_(i); the gate of switching element SWh receives the invertedsignal /b_(i). This type of switch can be effectively used when theanalog voltages to be switched are not too close to the low logic levelof the bit signals b_(i), /b_(i).

Switching elements SWh and SWl in FIG. 5C are transmission gatescombining PMOS and NMOS transistors. The PMOS transistor of switchingelement SWh and the NMOS transistor of switching element SWl receive acontrol signal representing bit b_(i); the NMOS transistor of switchingelement SWh and the PMOS transistor of switching element SWl receive theinverted signal /b_(i). This type of switch provides good switchingcharacteristics for all input voltages.

Depending on the voltage range of the analog output signal and thethreshold voltages of the PMOS and NMOS transistors, the configurationsin FIGS. 5A, 5B, and 5C can be used in various combinations. Onepreferable combination, since it minimizes the number of transistors,uses NMOS switching elements as in FIG. 5A in the lower selector 2 andPMOS switching elements as in FIG. 5B in the upper selector 3 andmidrange selectors 4, 5, 7. Another preferable combination usestransmission gates as in FIG. 5C in the lower selector 2 and PMOSswitching elements as in FIG. 5B in the upper selector 3 and midrangeselectors 4, 5, 7. Other potentially useful combinations include NMOSswitching elements in the lower and midrange selectors and PMOSswitching elements in the upper selectors, NMOS switching elements inthe lower and midrange selectors and transmission gates in the upperselectors, and NMOS switching elements in the lower selector,transmission gates in the midrange selectors, and PMOS switchingelements in the upper selector.

The switching-element transistors in the lower selector 2 and upperselector 3 may be formed in separate wells to avoid the degradation ofswitching characteristics caused by back bias.

As described above, the DAC according to this embodiment provides alower selector 2 and upper selector 3 that select voltages in thenonlinear upper and lower parts of the gray scale simply by decoding theinput digital input signal. For the linear middle portion of the grayscale, the DAC provides a pair of midrange selectors 4 and 5 that selecttwo voltages separated by a difference equivalent to 2^(k) gray levels,a midrange resistor string 6 that further divides this voltagedifference into 2^(k) levels, and a midrange output selector 7 thatselects a corresponding gray scale voltage from the further series ofdivided voltages. This configuration reduces the number of switchingelements needed to select gray levels, thereby reducing parasitic loads,and greatly reduces the number of resistors in resistor string 1.

The embodiment shown in FIG. 4 (in which n=6, m=3, and k=2) does notimply that six-bit DACs are the preferred application of the presentinvention. The invention is more applicable to DACs in which n is equalto or greater than eight, because the problems of the prior artdescribed earlier begin to appear at about n=8.

In a DAC with eight or more input bits, from considerations of devicesize and manufacturing variations, the number of resistors used in thelower range and upper range is preferably about 3% of the total numberof gray levels. Therefore, m=n−5 is preferable. If this condition issatisfied, the number of levels in the gray scale can be increased whilevariations in output accuracy are simultaneously reduced.

The values of n, m, and k in FIG. 2 can, however, be set arbitrarilyprovided the relationship 2≦k<m<n holds among them. For example, aneight-bit DAC can be configured with k=2, m=5, so that the lower andupper selectors 2 and 3 select voltages for the lower and upperthirty-two gray levels, respectively, and the midrange upper selector 4and midrange lower selector 5 select forty-eight midrange voltages eachat intervals of four gray levels.

An exemplary eight-bit DAC designed according to the present inventiontakes up about 40% less space than a conventional eight-bit DAC. As thenumber of bits to be converted increases, the space saving effectbecomes even greater.

The invention is not limited to the embodiment shown in FIG. 2; manyother variations are possible, including, for example, the following.

The midrange resistor string 6 may be replaced with a capacitive voltagedivider using capacitors.

The condition that k be less than m is not strictly necessary; k may beequal to m, or one greater than m.

More generally, the division into an upper range, a lower range, and amidrange may be made at arbitrary boundary values of the digital inputsignal. The voltage corresponding to one of the boundary values must beselected by both one of the upper and lower selectors and one of themidrange selectors, but this may be the upper boundary voltage insteadof the lower boundary voltage.

In FIG. 2, for example, the midrange lower selector 5 may selectvoltages from V2 ^(m) to V(2^(n)−2^(m)−2^(k)), and the midrange upperselector 4 may select voltages from V(2^(m)+2^(k)) to V(2^(n)−2^(m)),the selected voltages corresponding to digital input signal values inwhich the least significant k bits are all zero ‘0’.

The voltages generated by the first resistor string 1 need not beequally spaced in the midrange and unequally spaced in the upper andlower ranges. The S-shaped curve shown in FIG. 3 can be approximatedwith equally spaced voltages in the upper and lower ranges, for example,or the voltages may be unequally spaced in all three ranges, stillyielding analog output voltages that are spaced farther apart in theupper and lower ranges than in the midrange at the output terminal 8(OUT). The basic requirement is that the resistance values of theresistors in the upper and lower ranges of the first resistor string 1should be greater than the resistance values of the resistors in themidrange of the first resistance string 1 divided by the number N ofvoltages generated by the midrange resistor string 6 (in the aboveembodiment, N=2^(k)).

Those skilled in the art will recognize that further variations arepossible within the scope of the invention, which is defined in theappended claims.

1. A digital-to-analog converter for converting a digital input signalto an analog output voltage, comprising: a first resistor string forgenerating a series of voltages spanning an upper range, a lower range,and a midrange disposed between the upper range and the lower range; alower selector for selecting one of the voltages in the lower range asthe analog output voltage when the digital input signal has a valueequal to or less than a first boundary value; an upper selector forselecting one of the voltages in the upper range as the analog outputvoltage when the digital input signal has a value equal to or greaterthan a second boundary value; a pair of midrange selectors for selectinga mutually adjacent pair of voltages in the midrange when the digitalinput signal has a value between the first and second boundary values; amidrange voltage generator for generating a further series of voltagesbetween the pair of voltages selected by the pair of midrange selectors;and an output selector for selecting one of the voltages in the furtherseries of voltages as the analog output voltage when the digital inputsignal has a value strictly between the first and second boundaryvalues.
 2. The digital-to-analog converter of claim 1, wherein theanalog output voltages are spaced farther apart when the digital inputsignal has values equal to or less than the first boundary value, orequal to or greater than the second boundary value, than when thedigital input signal has values strictly between the first and secondboundary values.
 3. The digital-to-analog converter of claim 1, whereinthe resistor string comprises: a first sub-string of first resistors forgenerating the voltages in the upper range; a second sub-string ofsecond resistors for generating the voltages in the midrange; and athird sub-string of third resistors for generating the voltages in thelower range; and wherein the second sub-string being connected in seriesbetween the first sub-string and the third sub-string; the furtherseries of voltages consists of a number N of voltages; and the secondresistors and the third resistors have larger resistance values than theresistance values of the first resistors divided by the number N.
 4. Thedigital-to-analog converter of claim 1, wherein the midrange voltagegenerator comprises a second resistor string.
 5. The digital-to-analogconverter of claim 1, wherein each of the lower, upper, and midrangeselectors has a binary tree structure.
 6. The digital-to-analogconverter of claim 1, wherein: the lower selector comprises n-channelmetal-oxide-semiconductor (NMOS) transistors used as analog switchingelements; and the upper selector and the midrange selectors comprisep-channel metal-oxide-semiconductor (PMOS) transistors used as analogswitching elements.
 7. The digital-to-analog converter of claim 1,wherein: the lower selector comprises NMOS transistors and PMOStransistors used as transmission gates; and the upper selector and themidrange selectors comprise PMOS transistors used as analog switchingelements.
 8. The digital-to-analog converter of claim 1, wherein onevoltage generated by the first resistor string is selected both by oneof the lower selector and the upper selector and by one of the pair ofmidrange selectors.
 9. The digital-to-analog converter of claim 1,wherein the voltages selected by the lower selector, the upper selector,and the output selector are related to the values of the digital inputsignal by a gray scale correction curve.
 10. The digital-to-analogconverter of claim 1, wherein each of the digital input signal comprisesat least eight bits.
 11. The digital-to-analog converter of claim 10,wherein: each value of the digital input signal comprises n bits, nbeing a positive integer; the output selector is controlled by the leastsignificant k bits of the digital input signal, k being a positiveinteger less than n; and the further series of voltages comprisesequally spaced voltages equal in number to the k-th power of two. 12.The digital-to-analog converter of claim 1, wherein: each value of thedigital input signal comprises n bits, n being a positive integer; andthe number of voltages in the upper range is the m-th power of two, mbeing a positive integer less than n.
 13. The digital-to-analogconverter of claim 12, wherein m is equal to n minus five.
 14. Thedigital-to-analog converter of claim 12, wherein the upper selector iscontrolled by the m least significant bits of the digital input signaland operates when the n minus m most significant bits of the digitalinput signal are all ‘1’.
 15. The digital-to-analog converter of claim12, wherein: the number of voltages in the lower range is the m-th powerof two; and the lower selector is controlled by the m least significantbits of the digital input signal and operates when the n minus m mostsignificant bits of the digital input signal are all ‘0’.
 16. Thedigital-to-analog converter of claim 12, wherein the further series ofvoltages comprises equally spaced voltages equal in number to the k-thpower of two, k being another positive integer less than n.
 17. Thedigital-to-analog converter of claim 16, wherein k is less than m.